\>< P i K e P L a C e >:: [ Brain ]

This page was spawned by a series of discussions in Dec 2002 prior to several friends that were about to go through interviews. So herein lie some of the questions I consider interesting. Some of the problems don't have solutions with them. That means that if you think long enough, you should be able to get it. :)

Calendar Die

Commentary

Courtesy of Krish from an MS interview

Problem

You are given two blank cubes. You want to design a calendar such that every date can be represented by these cubes, ignoring the month, day of week, etc. How do you go about doing this?

Solution

The first thing you want to be able to do is represent the numbers 11 and 22, which would require a 1 and 2 on each cube. Now the cubes each have four faces left, and the next goal is to be able to take care of single digit numbers. This would require a 0 on each cube because neither cube will be able to contain all digits. That leaves three faces on each cube. A 3 can be placed on either cube since the only dates that need 3 to be represented are 03, 13, 23, 30, and 31. This leaves a total of five faces on the two cubes, with six numbers still needing to be placed: 4, 5, 6, 7, 8, and 9. However, 6 and 9 can be represented by a single face since one number can be created by flipping the other, only five of the six numbers need to be placed. Since both cubes have a 0, 1, and 2, these numbers can be placed arbitrarily on either cube.

Density

Commentary

Lutron Interview.

Problem

You are in a canoe with a 10lbs rock. If you throw the rock in the water, will the water level in the lake rise or fall (a miniscule amount)?

Hint

It does change.

Gold Coins I

Commentary

Courtesy Andrew Fall '02.

Problem

You have ten bags of gold coins with all coins of the same mass (say 1g), except in one bag (fool's gold?). You have a mass/scale (weighing machine?) you can use only once. How do you figure which bag is the bag with the fake coins?

Hint

Oh come on.

Solution

See Hint.

Gold Coins II

Commentary

Courtesy Andrew Fall '02.

Problem

Variant of the previous question. You still have ten bags, with some of different weights. With only one use of the scale, how do you figure out which bags have different weights?

Hint

Oh come on.

Solution

If you solved the previous question you should be able to solve this one too.

Light Bulbs

Commentary

Lutron Interview.

Problem

You have three light bulbs in one room. In another, separate room, you have three switches. Each switch is connected to one light bulb. You start out in the room with the switches, and you can play with them as much as you like. How do you figure out which switch controls which light if you can only go to the room with the light bulbs once?

Hint

Changing a light bulb after it's been on for a while is dangerous.

Pills

Commentary

Courtesy Keith Fall '02.

Problem

You have two bottles of pills: A and B. You need to have 1 of A and 1 of B. A and B look identical--you can't tell them apart. You pour 1 pill of A onto your palm, and proceed to pour 1 pill of B into your palm, but 2 come out. So now you have 2 B and 1 A in your palm and you can't tell them apart. What do you do?

Hint

You can cut pills in half.

Rectangles

Commentary

This one is apparently a popular interview question (it's a PM question). The Visual Studio GPM has rejected several full time candidates solely on the basis that they could not answer this question. And it's actually pretty simple.

Problem

Given a regular 8.5"x11" sheet of paper, you have a rectangle cut out of it somewhere on the sheet (you don't know size, orientation, placement, etc.) Using only one cut (think of those paper cutting boards), cut the sheet so that you have two equal masses. (Yes, you can fold it before cutting.)

Hint

How do you divide a rectangle into two equal pieces?

Solution

OK, you should be able to get the solution from the hint.

South, East, North

Commentary

Autodesk Interview.

Problem

At how many points on the earth can you go 10 miles south, 10 miles east, and 10 miles north, and end up on the same spot?

Hint

It's more than one.

Two Cars and a Hill

Commentary

Autodesk Interview.

Problem

You have a hill that's 6 miles length on one side, and 6 miles on the other. You have two cars A and B that start off at the same point, going to the other side of the hill. Car B leaves 12 minutes after A, which goes at 60mph. How fast does B have to go to make it to the other side before A does?

Hint

This question is easily calculable. The question is how much you doubt yourself.

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